Spontaneuous symmetry breaking in matrix models

Matrix models with rotational invariant weights provide, in the large $N$ limit, a robust universality of correlated eigenvalues. Here, we want to argue that a weight that breaks the eigenvalue distribution into disjoint supports, further induces a spontaneous breaking of the rotational symmetry. This SSB of the $U(N)$ can potentially be used as a toy model to study the eigenstate distribution at the Anderson Metal/Insulator Transition.